Clustered Graph Matching for Label Recovery and Graph Classification
Abstract
Given a collection of vertexaligned networks and an additional labelshuffled network, we propose procedures for leveraging the signal in the vertexaligned collection to recover the labels of the shuffled network. We consider matching the shuffled network to averages of the networks in the vertexaligned collection at different levels of granularity. We demonstrate both in theory and practice that if the graphs come from different network classes, then clustering the networks into classes followed by matching the new graph to clusteraverages can yield higher fidelity matching performance than matching to the global average graph. Moreover, by minimizing the graph matching objective function with respect to each cluster average, this approach simultaneously classifies and recovers the vertex labels for the shuffled graph. These theoretical developments are further reinforced via an illuminating real data experiment matching human connectomes.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 DOI:
 10.48550/arXiv.2205.03486
 arXiv:
 arXiv:2205.03486
 Bibcode:
 2022arXiv220503486L
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Machine Learning;
 Statistics  Methodology
 EPrint:
 22 pages, 8 figures, 5 tables